Are any of these tests signficant? How would they be written up in APA fomat?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Are any of these tests signficant? How would they be written up in APA fomat?
Transcribed Image Text:The table above presents the results of an ANOVA (Analysis of Variance) for energy. Here's a breakdown of the table contents:
- **Sum of Squares**: Represents the variation attributed to each source.
- **df (degrees of freedom)**: Indicates the number of independent values that can vary.
- **Mean Square**: Calculated by dividing the sum of squares by the respective degrees of freedom.
- **F**: The F-ratio, derived from dividing the mean square of each variable by the mean square of the residuals.
- **p**: The p-value, showing the statistical significance of the result.
- **η² (Eta squared)**: A measure of effect size.
### Breakdown:
- **Reference Group**:
- Sum of Squares: 36.6
- df: 1
- Mean Square: 36.6
- F: 0.0756
- p: 0.784
- η²: 0.001
- **Norm**:
- Sum of Squares: 177.8
- df: 1
- Mean Square: 177.8
- F: 0.3676
- p: 0.546
- η²: 0.005
- **Reference Group × Norm**:
- Sum of Squares: 1026.6
- df: 1
- Mean Square: 1026.6
- F: 2.1229
- p: 0.149
- η²: 0.026
- **Residuals**:
- Sum of Squares: 38201.8
- df: 79
- Mean Square: 483.6
This table helps determine whether there are significant differences between groups in terms of energy, but the high p-values suggest no statistically significant differences in this case.
Transcribed Image Text:**ANOVA - Mental Health**
| Source | Sum of Squares | df | Mean Square | F | p | η² |
|----------------------------|----------------|-----|-------------|------|------|-------|
| Reference Group | 110.0 | 1 | 110.0 | 0.199| 0.657| 0.002 |
| Norm | 75.8 | 1 | 75.8 | 0.137| 0.712| 0.002 |
| Reference Group ✻ Norm | 128.2 | 1 | 128.2 | 0.232| 0.631| 0.003 |
| Residuals | 44199.7 | 80 | 552.5 | | | |
- **Sum of Squares**: A measure of the total variability in the data.
- **df (degrees of freedom)**: The number of independent values or quantities that can vary.
- **Mean Square**: Calculated by dividing the sum of squares by the corresponding degrees of freedom.
- **F**: The ratio of two mean square values, indicating the variance between group means.
- **p**: The probability value, indicating the significance level of the results.
- **η²**: The effect size, representing the proportion of variance explained by each source.
The table provides a detailed analysis of variance for mental health data, showing how different factors contribute to overall variability. Each row represents a source of variance, and the interaction effect is indicated by "Reference Group ✻ Norm". Residuals account for unexplained variance.
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